Abstract: In this paper,according to the distribution of basic meteorological element field and simplifying the governing equation in low latitudes a nonlinear model which takes into consideration the equatorial β-plane approximation and describes the natural oscillation of the atmosphere has been set up.Applying this model the following problems are discussed:(l)The pure inertial oscillation without the influence of pressure field. (2)The iner al oscillation with the influence of pressure field which is assumed to be a symmetric function in y. (3) The stability of equilibrium point and the bifurcation phenomenon on certain condition. (4)The numerical results of the periodic variation for the zonal wind.It is shown that: (l)there exists the pure inertial oscillation only in the westerly current of tropical atmosphere,the angular frequency of linear oscillation is ω₀=√β₀μ₀^*(β₀ is the Rossby parameter,μ₀^*=μ₀-β₀y₀²/2,where μ₀ is the initial zonal velocity and y0 is the initial longitudinal position),the corresponding oscillatory period is 1-2 weeks. There are two kinds of angular frequency under the nonlinear condition,the one isω₀=√β₀μ₀,the other is ω₁=β₀y₀/2. However their effect on the results of linear oscillation is little,only when a soliton oscillator occurs (ω₁= ω₀),the oscillatory period increases rapidly,the low frequency and ultra-low frequency oscillations are emerged. (2)When the pressure field is considered the oscillation exists not only in westerly current but also in the weak easterly current. However this weak pressure field has little effect on the oscillatory period,it changes mainly the velues of inertial stability. (3)The stability of inertial oscillation depends on the linear inertial parameter μ. Under the linear condition,the inertial oscillation is stable when μ<0 and unstable when μ>0; but under the nonlinear condition,the stable oscillation also hap pens even μ>0,this is as a result of the damped action of the nonlinearity on the unstable growing. Therefore,as the parameter μ changes sign from negative to positive the supercritical bifurcation takes place in b<0 (b is the strength parameter of nonlinear oscillation).